Linear Geometric ICA: Fundamentals and Algorithms is a research paper published in Neural Computation (2003). On theSindex it has a DataRank of 3.2. It has been cited 69 times, with 44 citing works in its 1-hop citation network.
Geometric algorithms for linear independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (1995). We will reconsider geometric ICA in a theoretic framework showing that fixed points of geometric ICA fulfill a geometric convergence condition (GCC), which the mixed images of the unit vectors satisfy too. This leads to a conjecture claiming that in the nongaussian unimodal symmetric case, there is only one stable fixed point, implying the uniqueness of geometric ICA after convergence. Guided by the principles of ordinary geometric ICA, we then present a new approach to linear geometric ICA based on histograms observing a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost, by a factor of 100, compared to the ordinary geometric approach. Furthermore, we explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix, and compare geometric algorithms with classical ICA algorithms, namely, Extended Infomax and FastICA. Finally, we discuss the problem of high-dimensional data sets within the realm of geometrical ICA algorithms.
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Base Score Contribution
0.637
From this paper's citation signal
Citation Network Contribution
2.6
From 33 citing papers with measurable signal
Ranked by citation count — the same ordering the engine uses when summing log1p(Cq) over citers.
DataRank blends this paper's own citation count with the influence of the papers that cite it. Here, roughly 20% comes from its base citations and 80% from the citation network (33 citing papers contributed measurable signal).
Citers are pulled from OpenAlex sorted by cited_by_count:descand capped per paper, so when the cap binds we keep the highest-signal references and the score is reproducible across reruns.
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